Perhaps you too, have noticed that school graduates no longer know their times-tables, cannot add fractions or do long division? Even at [University name removed], we are finding that the students starting science and engineering degrees are not confident with standard mathematical skills.
Mathematics is the language of the physical world. Science and technology rely on mathematics. Studying mathematics develops sound reasoning, and has been a core discipline pursuing clarity of thought for thousands of years. So why are we presently failing to pass on this gift now?
1. What is wrong?
Maths teachers with over twenty years experience in Queensland, and those teachers who have also taught in other systems, can readily explain what is wrong with our school system:
The reason students do not know their times-tables is because our teachers of maths have been instructed not to have students memorise facts! The reason students do not know how to add fractions, and do not know how to do long division, and do not have confidence in doing mathematical procedures, is because teachers of maths, at all school levels, have been instructed to de-emphasize the standard algorithms, and not to use repetition.
No, it’s not a terrorist giving our teachers these instructions. It’s the recent fashion of educational ideology endorsed by our educational theorists. This ideology is attributed to the 1950s psychologist, Bloom. He regards activities such as remembering and understanding as ‘lower order’ while activities like application and evaluation are considered ‘higher order’.
Bloom’s theory of ‘higher-order-thinking’ may have appeal in some sectors, but it is not suited to mathematics, since mathematics, much like learning to play a musical instrument, requires years of practice and repetition. Following Bloom, our school maths has become instead, like one of those ‘musical appreciation courses’ where students are briefly exposed to a sweeping range of topics, but never really learn themselves, how to play. Would you rather hear your child say “some people can do it” or hear them say “I can do it”?
With our emphasis on so-called ‘higher-order’ thinking, we have neglected the basics. This has been disastrous for learning maths as maths builds upon itself from one year to the next: Calculus relies on advanced algebra, which relies on simple algebra, which relies on standard arithmetic, which relies on knowledge of the times-tables. Only half-knowing maths one year means only one-quarter-knowing it the next year, and only one-eighth-knowing it the year after that, and so on, until you’re having nightmares about arriving at school on the day of the exam, completely unprepared and without any clothes on.
I can’t help but think that Bloom’s followers will not consider maths as ‘higher-order’ until they have turned maths into something it is not. It appears to me that university-level mathematics is still considered a ‘lower-order’ activity according to Bloom’s taxonomy.
Bloom’s ideology also inhibits developing maths skills in our schools through the introduction of written assignments in maths, and the insistence on use of muti-media and technology. These things do not build basic mathematical skills, anywhere nearly as well as doing regular homework and studying for an exam. Written assignments keep everyone busy, and basic maths is left out.
High school Chemistry and Physics are also now being distorted by the inappropriate introduction of very long written assignments.
The imposition of Bloom’s ideology also creates much red tape. The paperwork requirements placed on teachers waste so much time that they are obstructive to students’ learning. For example, when a teacher marks a maths test, he/she is forbidden from the standard practice of awarding a (number) mark for each question and adding these up to get a total score.
Instead, for each question, teachers must award letter grades, over three different categories. The appropriate letter is to be chosen by reading and considering perhaps fifty (50) paragraphs of descriptors. To give you an idea, here is one such paragraph:
“The student work has the following characteristics:
use of problem solving strategies to interpret, clarify and analyze problems to develop responses to routine and non-routine simple tasks in life-related or abstract situations”
So a task, which is done by every teacher, for every student, on every piece of assessment, which should be simple and routine, is in Queensland, not simple at all, but instead a festival of cultural deliberation, After all these ‘festivities’, the mystery of how to combine the letter grades begins. Later on, this combination emerges somehow transfigured, on the report to parents, as one of maybe five uncomfortably-worded sentences. The whole process proceeds officially uncontaminated by numbers.
” How is Johnny going in maths?” remains the question on everyone’s lips.
2. How can we fix it?
This article has briefly indicated how the imposition of Bloom’s ideology on our teachers, has prevented a generation of our youth from gaining maths skills.
‘Education theory’ and Psychology are relatively new and speculative areas of study, purporting frequently changing ideas. In hindsight, we might question why we ever placed an educational theorist into a position of authority over the learning mathematics. It doesn’t seem appropriate to subject a whole population to unproven ideas of a speculative nature. People have been learning mathematics for thousands of years. One would think that traditional approaches would be safer and more reliable.
The key to fixing this problem is to have experts in the actual discipline of study responsible for the curriculum and assessment of that discipline, rather than appointing those who imagine that every kind of learning is the same. When it comes to mathematics, an appropriate panel of experts might consist of very experienced maths teachers, engineers and mathematicians. Physicists, chemists and Economists might also suit. (Caution: degrees called ‘mathematics education’ generally consist of only a little or no mathematics, and a lot of ‘education’.)
However we decide to restructure, and who ever we appoint, the new body governing mathematics in school must be answerable to someone, unlike the Queensland Studies Authority, which was set up as a statutory body, answerable only to itself.
I feel that we should keep state sovereignty over education as much as possible, even though the proposed national curriculum looks better than our present one. My reason for this is, that if or when the national education bodies begin to move down silly paths, then it will be so much more difficult to turn them around. Will the national body appoint people who do mathematics, or people who do education?
To conclude, there is some good news:
We can be sure that our current low performance in maths is not due to any intrinsic or innate stupidity,
- this problem can be solved, and
- it is not an issue of needing to spend more time or money.
A good mathematics course will build a student’s confidence in his or her own ability to reason clearly and correctly. After completion, a student may go on to apply this ability to his or her chosen pursuits in life. Shall we pass on this gift to the next generation?